# Questions tagged [logspace]

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### Is there a construction which multiplies and adds spanning trees in Logspace?

I.1 Suppose we have two planar graphs $G_1$ and $G_2$ with spanning tree count $C_1$ and $C_2$ respectively then is there a graph construction in Logspace to get a planar graph from $G_1$ and $G_2$ ...
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### One way analogues of Logspace

When we say a function is one-way we typically mean a function is encodable in $P$ but its decryption is not in $P$ but in $UP$. Likewise we say a function is logspace one-way if the function is ...
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### Gurevich's theorem on primitive recursive functions being logspace-computable

I recently came across the following result attributed to Gurevich, according to which I understood that the class of problems solvable by primitive recursive functions is precisely the class L of ...
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### Simultaneous evidence for $L\neq NL$ and $P\neq NP$

We believe $L\neq NL$ and $P\neq NP$. Is there any evidence which simultaneously imply $L\neq NL$ and $P\neq NP$?
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### $CH=UL$ and partial breaking of transitive closure bottleneck problem and Savitch's theorem?

Let $L^t=DSPACE[O(\log n)^t]$, $NL^t=NSPACE[O(\log n)^t]$ and $UL^t=USPACE[O(\log n)^t$. Savitch provides $NL\subseteq L^{2}$. If $CH=UL$ we clearly got rid of the transitive closure bottleneck ...
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### It is known that $L \subsetneq PH$?

Is it known whether $Logspace$ is strictly contained in the polynomial time hierarchy ? Are there oracles relative to which these classes are equal / distinct ?
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### Number theoretic problems complete for $\mathsf{RL}$

Are there number theoretic problems (such as those related to $\mathsf{gcd}$) that are in $\mathsf{RL}$? Can these also be $\mathsf{RL}$-complete problems (is there any $\mathsf{RL}$-complete ... 98 views

### Are there any non-relativized separations between $L$ and $PH$?

In one sense, $P$ vs. $PSPACE$ is the "easiest" first step to showing $P \neq NP$... and this is one you hear often about. In a different sense, you could take $L$ at one end and then $PH$ at the ...
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### What is the power of general poly-size permutation branching programs?

Call $\mathsf{PPBP}$ the class of languages decided by poly-size families of permutation branching programs, which are layered branching programs (i.e., the ones defined here) whose transitions ...
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### What is the space complexity of computing the eigenvectors of a matrix?

By the answer to this question, computing the eigenvalues of a matrix to within $2^{-n}$ precision can be done in polylogarithmic space. Is it also possible to compute the eigenvectors of a matrix to ...
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### Any known connections between open problems for time and space: P vs L, NP vs NL, BPP vs BPL, ⊕P vs ⊕L

It would be nice to show that $P=L$ implies $NP=NL$. Or, $NP=NL$ implies $UP=UL$. Or maybe, $⊕P = ⊕L$ implies $PP = PL$. Are there any known connections between the problems: P vs L, UP vs UL, NP ...
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### Complexity of the search version of 2-SAT assuming $\mathsf{L = NL}$

If $\mathsf{L = NL}$, then there is a logspace algorithm that solves the decision version of 2-SAT. Is $\mathsf{L = NL}$ known to imply that there is a logspace algorithm to obtain a satisfying ... 263 views

### Why can't Horn-SAT be solved in Log-space? [closed]

A simple algorithm for Horn-SAT (in CNF) is the following: Given: A Horn formula $\phi$ in CNF. Find a unit clause (a clause with one literal) $C_i$. $~$Set the variable $x_j$ appearing in $C_i$ to ...
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### Does ${\bf AC^0PAD} = {\bf PPAD}$?

What happens if we define ${\bf PPAD}$ such that instead of a polytime Turing-machine/polysize circuit, a logspace Turing-machine or an ${\bf AC^0}$ circuit encodes the problem? Recently giving ...
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### What if an $\mathsf L$-complete problem has $\mathsf{NC}^1$ circuits? More generally, what evidence is there against $\mathsf{NC}^1=\mathsf{L}$?

Edit: let me reformulate the question in a more specific way (and change the title accordingly). A slightly edited version of the original question follows. Is there a result comparable to the Karp-...
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### Large classes which contain LOGSPACE for which strict inclusions are unknown

The wikipedia page on PSPACE mentions that the inclusion $NL\subset PH$ is not known to be strict (unfortunately without references). Q1: What about $L\subset PH$ and $L\subset P^{\#P}$ - are these ...
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### Detecting undirected cycles in logarithmic space [closed]

I have a lot of difficulties with constructing algorithms that use $O(\log n)$ space, as I am unsure about how much can be stored on the worktape. I am trying to figure out an algorithm for the ...
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### Two way deterministic multihead counter automata or logspace TM with counter

Is that known something about languages recognized by two-way deterministic multihead counter automaton or logspace TM with counter (equivalent model)? This class called Aux2DC in my advisor's paper. ...